This dissertation considers an American put option written on a single underlying
which does not pay dividends, for which no closed form solution exists. As a conse-
quence, numerical techniques have been developed to estimate the value of the Amer-
ican put option. These include analytical approximations, tree or lattice methods,
¯nite di®erence methods, Monte Carlo simulation and integral representations. We
¯rst present the mathematical descriptions underlying these numerical techniques.
We then provide an examination of a selection of algorithms from each technique,
including implementation details, possible enhancements and a description of the
convergence behaviour. Finally, we compare the estimates and the execution times
of each of the algorithms considered.